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» On Bounds for the k-Partitioning of Graphs
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ISAAC
2004
Springer
141views Algorithms» more  ISAAC 2004»
15 years 3 months ago
Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation
We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-complete in planar graphs, even if they a...
Jérôme Monnot, Vangelis Th. Paschos, ...
SIAMDM
2008
148views more  SIAMDM 2008»
14 years 10 months ago
A New Algorithm for On-line Coloring Bipartite Graphs
We first show that for any bipartite graph H with at most five vertices, there exists an on-line competitive algorithm for the class of H-free bipartite graphs. We then analyze th...
Hajo Broersma, Agostino Capponi, Daniël Paulu...
ENDM
2008
118views more  ENDM 2008»
14 years 10 months ago
Number of Crossing-Free Geometric Graphs vs. Triangulations
We show that there is a constant > 0 such that, for any set P of n 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at...
Andreas Razen, Jack Snoeyink, Emo Welzl
SODA
2003
ACM
103views Algorithms» more  SODA 2003»
14 years 11 months ago
On the rectilinear crossing number of complete graphs
We prove a lower bound of 0.3288   n 4¡ for the rectilinear crossing number cr(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadril...
Uli Wagner
DIALM
2008
ACM
179views Algorithms» more  DIALM 2008»
14 years 11 months ago
Distance graphs: from random geometric graphs to Bernoulli graphs and between
A random geometric graph G(n, r) is a graph resulting from placing n points uniformly at random on the unit area disk, and connecting two points iff their Euclidean distance is at ...
Chen Avin